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Number Systems

Short Answer Type

51. Find one irrational number between the numbers a and b given below:

a = 0.1111 ........ =

0. top enclose 1

b = 0.1101.

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52. Find two rational numbers in the form

straight p over straight q

between 0.34 344 3444 34444 3 ...... and 0.36 366 3666 36666 3......

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53. Express $5. top enclose 347$ in the form $straight p over straight q$ where p and q are integers and q ≠ 0.

$Let space straight x space equals space 5. top enclose 347$

⇒ x = 5.3474747......

⇒ 10x = 53.474747...... ...(1)

⇒ 1000x = 5347.474747...... ...(2)

Subtracting (1) from (2), we get

990x = 5294
$rightwards double arrow space space straight x space 5294 over 990 rightwards double arrow space space space straight x space equals space 2647 over 495 rightwards double arrow space space space straight p space equals space 2647 comma space space space space straight q space equals space 495 space space left parenthesis not equal to 0 right parenthesis$